Kinetic titration

The kinetic titration (single cycle kinetics) is useful with interactions which are difficult to regenerate or when regeneration is detrimental to the ligand (1). In addition, it can be used to determine the concentration and kinetic range of an interaction. During the kinetic titration, the analyte is injected from a low to high concentration with short dissociation times in between and a long dissociation time at the end. The short and long dissociation times will speed up the injection sequence.
All the analyte injections are analysed in the same sensorgram with a special equation for kinetic titration. The model is based on the one to one binding interaction and is limited to five analyte injections (2). A mass transfer component (kt) and drift are added in de model.

Kinetic titration

Reaction equation

Reaction equation

Differential equation

Differential equation

Response calculation

Response calculation

Because it is not possible to solve this type of injection with a differential model, a numeric model is used. In the numerical model each analyte injection is individually fit, and the total response calculated. The numerical modal also contains terms for mass transport, drift and bulk refractive index mismatches.

Numeric model

Numeric model

Parameter setup

Name

Fit

Allow Neg.

Keyword

Initial value

Units

ka

global

No

No

1e5

M-1 s-1

kd

global

No

No

1e-3

s-1

Rmax

local

No

No

YMax

RU

kt

global

No

No

2e7

RU M-1 s-1

RI1

local

Yes

No

0

RU

RI2

local

Yes

No

0

RU

RI3

local

Yes

No

0

RU

RI4

local

Yes

No

0

RU

RI5

local

Yes

No

0

RU

Conc

No

No

Yes

M

ton1

No

No

Yes

s

ton2

No

No

Yes

s

ton3

No

No

Yes

s

ton4

No

No

Yes

s

ton5

No

No

Yes

s

c-time

No

No

Yes

s

F

No

No

Yes

Drift

Local

Yes

No

0

RU s-1

Although in the parameter table the RI and Drift are locally fit, they are in the model set to a constant of zero. It is better to start to fit the curves without these parameters. When the kinetic parameters are known, then it is possible to add refractive index bulk effect or drift.

Report setup

Name

Value

Units

ka

ka

M-1s-1

kd

kd

s-1

KD

kd/ka

M

Rmax

Rmax

RU

kt

kt

RU M-1s-1

RI1

RI1

RU

RI2

RI2

RU

RI3

RI3

RU

RI4

RI4

RU

RI5

RI5

RU

Drift

Drift

RU s-1

Below an example of a sensorgram generated with the differential equations from above.